>> In many cases, equality of functions has been decided by humans,
>> as has
>> termination of programs. Of course this doesn't prove that humans
>> can, in
>> principle, decide equality for any pair of functions. But neither
>> has the
>> opposite been proved.
>> It hasn't been proved that we can't build a device that can decide
> equality for arbitrary functions, either.
I'm sure it can be proved that any mathematical problem can be
reduced to equality of two functions, so our ability to decide it
contradicts Goedel theorem.